Properties

Label 855.2.k.f.406.2
Level $855$
Weight $2$
Character 855.406
Analytic conductor $6.827$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [855,2,Mod(406,855)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(855, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 0, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("855.406");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 855 = 3^{2} \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 855.k (of order \(3\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(6.82720937282\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{2}, \sqrt{-3})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} + 2x^{2} + 4 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 285)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 406.2
Root \(0.707107 + 1.22474i\) of defining polynomial
Character \(\chi\) \(=\) 855.406
Dual form 855.2.k.f.676.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.20711 + 2.09077i) q^{2} +(-1.91421 + 3.31552i) q^{4} +(-0.500000 - 0.866025i) q^{5} -3.82843 q^{7} -4.41421 q^{8} +O(q^{10})\) \(q+(1.20711 + 2.09077i) q^{2} +(-1.91421 + 3.31552i) q^{4} +(-0.500000 - 0.866025i) q^{5} -3.82843 q^{7} -4.41421 q^{8} +(1.20711 - 2.09077i) q^{10} -2.82843 q^{11} +(-1.91421 + 3.31552i) q^{13} +(-4.62132 - 8.00436i) q^{14} +(-1.50000 - 2.59808i) q^{16} +(-3.41421 - 5.91359i) q^{17} +(4.00000 + 1.73205i) q^{19} +3.82843 q^{20} +(-3.41421 - 5.91359i) q^{22} +(2.41421 - 4.18154i) q^{23} +(-0.500000 + 0.866025i) q^{25} -9.24264 q^{26} +(7.32843 - 12.6932i) q^{28} +(-0.828427 + 1.43488i) q^{29} -5.00000 q^{31} +(-0.792893 + 1.37333i) q^{32} +(8.24264 - 14.2767i) q^{34} +(1.91421 + 3.31552i) q^{35} -7.82843 q^{37} +(1.20711 + 10.4539i) q^{38} +(2.20711 + 3.82282i) q^{40} +(-1.41421 - 2.44949i) q^{41} +(-1.08579 - 1.88064i) q^{43} +(5.41421 - 9.37769i) q^{44} +11.6569 q^{46} +(-4.41421 + 7.64564i) q^{47} +7.65685 q^{49} -2.41421 q^{50} +(-7.32843 - 12.6932i) q^{52} +(-1.00000 + 1.73205i) q^{53} +(1.41421 + 2.44949i) q^{55} +16.8995 q^{56} -4.00000 q^{58} +(-7.15685 + 12.3960i) q^{61} +(-6.03553 - 10.4539i) q^{62} -9.82843 q^{64} +3.82843 q^{65} +(5.74264 - 9.94655i) q^{67} +26.1421 q^{68} +(-4.62132 + 8.00436i) q^{70} +(5.00000 + 8.66025i) q^{71} +(3.74264 + 6.48244i) q^{73} +(-9.44975 - 16.3674i) q^{74} +(-13.3995 + 9.94655i) q^{76} +10.8284 q^{77} +(7.32843 + 12.6932i) q^{79} +(-1.50000 + 2.59808i) q^{80} +(3.41421 - 5.91359i) q^{82} +8.00000 q^{83} +(-3.41421 + 5.91359i) q^{85} +(2.62132 - 4.54026i) q^{86} +12.4853 q^{88} +(-2.24264 + 3.88437i) q^{89} +(7.32843 - 12.6932i) q^{91} +(9.24264 + 16.0087i) q^{92} -21.3137 q^{94} +(-0.500000 - 4.33013i) q^{95} +(3.00000 + 5.19615i) q^{97} +(9.24264 + 16.0087i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 2 q^{2} - 2 q^{4} - 2 q^{5} - 4 q^{7} - 12 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 2 q^{2} - 2 q^{4} - 2 q^{5} - 4 q^{7} - 12 q^{8} + 2 q^{10} - 2 q^{13} - 10 q^{14} - 6 q^{16} - 8 q^{17} + 16 q^{19} + 4 q^{20} - 8 q^{22} + 4 q^{23} - 2 q^{25} - 20 q^{26} + 18 q^{28} + 8 q^{29} - 20 q^{31} - 6 q^{32} + 16 q^{34} + 2 q^{35} - 20 q^{37} + 2 q^{38} + 6 q^{40} - 10 q^{43} + 16 q^{44} + 24 q^{46} - 12 q^{47} + 8 q^{49} - 4 q^{50} - 18 q^{52} - 4 q^{53} + 28 q^{56} - 16 q^{58} - 6 q^{61} - 10 q^{62} - 28 q^{64} + 4 q^{65} + 6 q^{67} + 48 q^{68} - 10 q^{70} + 20 q^{71} - 2 q^{73} - 18 q^{74} - 14 q^{76} + 32 q^{77} + 18 q^{79} - 6 q^{80} + 8 q^{82} + 32 q^{83} - 8 q^{85} + 2 q^{86} + 16 q^{88} + 8 q^{89} + 18 q^{91} + 20 q^{92} - 40 q^{94} - 2 q^{95} + 12 q^{97} + 20 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/855\mathbb{Z}\right)^\times\).

\(n\) \(172\) \(191\) \(496\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{1}{3}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.20711 + 2.09077i 0.853553 + 1.47840i 0.877981 + 0.478696i \(0.158890\pi\)
−0.0244272 + 0.999702i \(0.507776\pi\)
\(3\) 0 0
\(4\) −1.91421 + 3.31552i −0.957107 + 1.65776i
\(5\) −0.500000 0.866025i −0.223607 0.387298i
\(6\) 0 0
\(7\) −3.82843 −1.44701 −0.723505 0.690319i \(-0.757470\pi\)
−0.723505 + 0.690319i \(0.757470\pi\)
\(8\) −4.41421 −1.56066
\(9\) 0 0
\(10\) 1.20711 2.09077i 0.381721 0.661160i
\(11\) −2.82843 −0.852803 −0.426401 0.904534i \(-0.640219\pi\)
−0.426401 + 0.904534i \(0.640219\pi\)
\(12\) 0 0
\(13\) −1.91421 + 3.31552i −0.530907 + 0.919558i 0.468442 + 0.883494i \(0.344815\pi\)
−0.999349 + 0.0360643i \(0.988518\pi\)
\(14\) −4.62132 8.00436i −1.23510 2.13926i
\(15\) 0 0
\(16\) −1.50000 2.59808i −0.375000 0.649519i
\(17\) −3.41421 5.91359i −0.828068 1.43426i −0.899551 0.436815i \(-0.856107\pi\)
0.0714831 0.997442i \(-0.477227\pi\)
\(18\) 0 0
\(19\) 4.00000 + 1.73205i 0.917663 + 0.397360i
\(20\) 3.82843 0.856062
\(21\) 0 0
\(22\) −3.41421 5.91359i −0.727913 1.26078i
\(23\) 2.41421 4.18154i 0.503398 0.871911i −0.496594 0.867983i \(-0.665416\pi\)
0.999992 0.00392850i \(-0.00125049\pi\)
\(24\) 0 0
\(25\) −0.500000 + 0.866025i −0.100000 + 0.173205i
\(26\) −9.24264 −1.81263
\(27\) 0 0
\(28\) 7.32843 12.6932i 1.38494 2.39879i
\(29\) −0.828427 + 1.43488i −0.153835 + 0.266450i −0.932634 0.360823i \(-0.882496\pi\)
0.778799 + 0.627273i \(0.215829\pi\)
\(30\) 0 0
\(31\) −5.00000 −0.898027 −0.449013 0.893525i \(-0.648224\pi\)
−0.449013 + 0.893525i \(0.648224\pi\)
\(32\) −0.792893 + 1.37333i −0.140165 + 0.242773i
\(33\) 0 0
\(34\) 8.24264 14.2767i 1.41360 2.44843i
\(35\) 1.91421 + 3.31552i 0.323561 + 0.560424i
\(36\) 0 0
\(37\) −7.82843 −1.28699 −0.643493 0.765452i \(-0.722515\pi\)
−0.643493 + 0.765452i \(0.722515\pi\)
\(38\) 1.20711 + 10.4539i 0.195819 + 1.69584i
\(39\) 0 0
\(40\) 2.20711 + 3.82282i 0.348974 + 0.604441i
\(41\) −1.41421 2.44949i −0.220863 0.382546i 0.734207 0.678925i \(-0.237554\pi\)
−0.955070 + 0.296379i \(0.904221\pi\)
\(42\) 0 0
\(43\) −1.08579 1.88064i −0.165581 0.286794i 0.771281 0.636495i \(-0.219617\pi\)
−0.936861 + 0.349701i \(0.886283\pi\)
\(44\) 5.41421 9.37769i 0.816223 1.41374i
\(45\) 0 0
\(46\) 11.6569 1.71871
\(47\) −4.41421 + 7.64564i −0.643879 + 1.11523i 0.340680 + 0.940179i \(0.389343\pi\)
−0.984559 + 0.175052i \(0.943991\pi\)
\(48\) 0 0
\(49\) 7.65685 1.09384
\(50\) −2.41421 −0.341421
\(51\) 0 0
\(52\) −7.32843 12.6932i −1.01627 1.76023i
\(53\) −1.00000 + 1.73205i −0.137361 + 0.237915i −0.926497 0.376303i \(-0.877195\pi\)
0.789136 + 0.614218i \(0.210529\pi\)
\(54\) 0 0
\(55\) 1.41421 + 2.44949i 0.190693 + 0.330289i
\(56\) 16.8995 2.25829
\(57\) 0 0
\(58\) −4.00000 −0.525226
\(59\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(60\) 0 0
\(61\) −7.15685 + 12.3960i −0.916341 + 1.58715i −0.111416 + 0.993774i \(0.535539\pi\)
−0.804926 + 0.593376i \(0.797795\pi\)
\(62\) −6.03553 10.4539i −0.766514 1.32764i
\(63\) 0 0
\(64\) −9.82843 −1.22855
\(65\) 3.82843 0.474858
\(66\) 0 0
\(67\) 5.74264 9.94655i 0.701575 1.21516i −0.266338 0.963880i \(-0.585814\pi\)
0.967913 0.251284i \(-0.0808529\pi\)
\(68\) 26.1421 3.17020
\(69\) 0 0
\(70\) −4.62132 + 8.00436i −0.552353 + 0.956704i
\(71\) 5.00000 + 8.66025i 0.593391 + 1.02778i 0.993772 + 0.111434i \(0.0355445\pi\)
−0.400381 + 0.916349i \(0.631122\pi\)
\(72\) 0 0
\(73\) 3.74264 + 6.48244i 0.438043 + 0.758713i 0.997539 0.0701207i \(-0.0223384\pi\)
−0.559496 + 0.828833i \(0.689005\pi\)
\(74\) −9.44975 16.3674i −1.09851 1.90268i
\(75\) 0 0
\(76\) −13.3995 + 9.94655i −1.53703 + 1.14095i
\(77\) 10.8284 1.23401
\(78\) 0 0
\(79\) 7.32843 + 12.6932i 0.824512 + 1.42810i 0.902291 + 0.431127i \(0.141884\pi\)
−0.0777789 + 0.996971i \(0.524783\pi\)
\(80\) −1.50000 + 2.59808i −0.167705 + 0.290474i
\(81\) 0 0
\(82\) 3.41421 5.91359i 0.377037 0.653047i
\(83\) 8.00000 0.878114 0.439057 0.898459i \(-0.355313\pi\)
0.439057 + 0.898459i \(0.355313\pi\)
\(84\) 0 0
\(85\) −3.41421 + 5.91359i −0.370323 + 0.641419i
\(86\) 2.62132 4.54026i 0.282664 0.489589i
\(87\) 0 0
\(88\) 12.4853 1.33094
\(89\) −2.24264 + 3.88437i −0.237719 + 0.411742i −0.960060 0.279796i \(-0.909733\pi\)
0.722340 + 0.691538i \(0.243067\pi\)
\(90\) 0 0
\(91\) 7.32843 12.6932i 0.768228 1.33061i
\(92\) 9.24264 + 16.0087i 0.963612 + 1.66902i
\(93\) 0 0
\(94\) −21.3137 −2.19834
\(95\) −0.500000 4.33013i −0.0512989 0.444262i
\(96\) 0 0
\(97\) 3.00000 + 5.19615i 0.304604 + 0.527589i 0.977173 0.212445i \(-0.0681426\pi\)
−0.672569 + 0.740034i \(0.734809\pi\)
\(98\) 9.24264 + 16.0087i 0.933648 + 1.61713i
\(99\) 0 0
\(100\) −1.91421 3.31552i −0.191421 0.331552i
\(101\) −8.07107 + 13.9795i −0.803101 + 1.39101i 0.114464 + 0.993427i \(0.463485\pi\)
−0.917565 + 0.397585i \(0.869848\pi\)
\(102\) 0 0
\(103\) 4.17157 0.411037 0.205519 0.978653i \(-0.434112\pi\)
0.205519 + 0.978653i \(0.434112\pi\)
\(104\) 8.44975 14.6354i 0.828566 1.43512i
\(105\) 0 0
\(106\) −4.82843 −0.468978
\(107\) −14.0000 −1.35343 −0.676716 0.736245i \(-0.736597\pi\)
−0.676716 + 0.736245i \(0.736597\pi\)
\(108\) 0 0
\(109\) −2.65685 4.60181i −0.254480 0.440773i 0.710274 0.703926i \(-0.248571\pi\)
−0.964754 + 0.263152i \(0.915238\pi\)
\(110\) −3.41421 + 5.91359i −0.325532 + 0.563839i
\(111\) 0 0
\(112\) 5.74264 + 9.94655i 0.542629 + 0.939860i
\(113\) −4.00000 −0.376288 −0.188144 0.982141i \(-0.560247\pi\)
−0.188144 + 0.982141i \(0.560247\pi\)
\(114\) 0 0
\(115\) −4.82843 −0.450253
\(116\) −3.17157 5.49333i −0.294473 0.510042i
\(117\) 0 0
\(118\) 0 0
\(119\) 13.0711 + 22.6398i 1.19822 + 2.07538i
\(120\) 0 0
\(121\) −3.00000 −0.272727
\(122\) −34.5563 −3.12858
\(123\) 0 0
\(124\) 9.57107 16.5776i 0.859507 1.48871i
\(125\) 1.00000 0.0894427
\(126\) 0 0
\(127\) 10.4853 18.1610i 0.930418 1.61153i 0.147811 0.989016i \(-0.452777\pi\)
0.782607 0.622516i \(-0.213889\pi\)
\(128\) −10.2782 17.8023i −0.908471 1.57352i
\(129\) 0 0
\(130\) 4.62132 + 8.00436i 0.405317 + 0.702029i
\(131\) −5.24264 9.08052i −0.458052 0.793369i 0.540806 0.841147i \(-0.318119\pi\)
−0.998858 + 0.0477784i \(0.984786\pi\)
\(132\) 0 0
\(133\) −15.3137 6.63103i −1.32787 0.574983i
\(134\) 27.7279 2.39533
\(135\) 0 0
\(136\) 15.0711 + 26.1039i 1.29233 + 2.23839i
\(137\) 3.24264 5.61642i 0.277037 0.479843i −0.693610 0.720351i \(-0.743981\pi\)
0.970647 + 0.240508i \(0.0773140\pi\)
\(138\) 0 0
\(139\) −3.15685 + 5.46783i −0.267761 + 0.463775i −0.968283 0.249855i \(-0.919617\pi\)
0.700522 + 0.713630i \(0.252950\pi\)
\(140\) −14.6569 −1.23873
\(141\) 0 0
\(142\) −12.0711 + 20.9077i −1.01298 + 1.75454i
\(143\) 5.41421 9.37769i 0.452759 0.784202i
\(144\) 0 0
\(145\) 1.65685 0.137594
\(146\) −9.03553 + 15.6500i −0.747786 + 1.29520i
\(147\) 0 0
\(148\) 14.9853 25.9553i 1.23178 2.13351i
\(149\) −3.41421 5.91359i −0.279703 0.484460i 0.691608 0.722273i \(-0.256903\pi\)
−0.971311 + 0.237813i \(0.923569\pi\)
\(150\) 0 0
\(151\) 21.6569 1.76241 0.881205 0.472735i \(-0.156733\pi\)
0.881205 + 0.472735i \(0.156733\pi\)
\(152\) −17.6569 7.64564i −1.43216 0.620143i
\(153\) 0 0
\(154\) 13.0711 + 22.6398i 1.05330 + 1.82436i
\(155\) 2.50000 + 4.33013i 0.200805 + 0.347804i
\(156\) 0 0
\(157\) 7.08579 + 12.2729i 0.565507 + 0.979487i 0.997002 + 0.0773721i \(0.0246529\pi\)
−0.431495 + 0.902115i \(0.642014\pi\)
\(158\) −17.6924 + 30.6441i −1.40753 + 2.43791i
\(159\) 0 0
\(160\) 1.58579 0.125367
\(161\) −9.24264 + 16.0087i −0.728422 + 1.26166i
\(162\) 0 0
\(163\) −13.1421 −1.02937 −0.514686 0.857379i \(-0.672091\pi\)
−0.514686 + 0.857379i \(0.672091\pi\)
\(164\) 10.8284 0.845558
\(165\) 0 0
\(166\) 9.65685 + 16.7262i 0.749517 + 1.29820i
\(167\) 4.48528 7.76874i 0.347081 0.601163i −0.638648 0.769499i \(-0.720506\pi\)
0.985730 + 0.168336i \(0.0538394\pi\)
\(168\) 0 0
\(169\) −0.828427 1.43488i −0.0637252 0.110375i
\(170\) −16.4853 −1.26436
\(171\) 0 0
\(172\) 8.31371 0.633914
\(173\) −7.65685 13.2621i −0.582140 1.00830i −0.995225 0.0976036i \(-0.968882\pi\)
0.413086 0.910692i \(-0.364451\pi\)
\(174\) 0 0
\(175\) 1.91421 3.31552i 0.144701 0.250629i
\(176\) 4.24264 + 7.34847i 0.319801 + 0.553912i
\(177\) 0 0
\(178\) −10.8284 −0.811625
\(179\) 12.1421 0.907546 0.453773 0.891117i \(-0.350078\pi\)
0.453773 + 0.891117i \(0.350078\pi\)
\(180\) 0 0
\(181\) −1.34315 + 2.32640i −0.0998352 + 0.172920i −0.911616 0.411042i \(-0.865165\pi\)
0.811781 + 0.583962i \(0.198498\pi\)
\(182\) 35.3848 2.62289
\(183\) 0 0
\(184\) −10.6569 + 18.4582i −0.785634 + 1.36076i
\(185\) 3.91421 + 6.77962i 0.287779 + 0.498447i
\(186\) 0 0
\(187\) 9.65685 + 16.7262i 0.706179 + 1.22314i
\(188\) −16.8995 29.2708i −1.23252 2.13479i
\(189\) 0 0
\(190\) 8.44975 6.27231i 0.613009 0.455041i
\(191\) 11.1716 0.808347 0.404173 0.914682i \(-0.367559\pi\)
0.404173 + 0.914682i \(0.367559\pi\)
\(192\) 0 0
\(193\) −7.39949 12.8163i −0.532627 0.922538i −0.999274 0.0380938i \(-0.987871\pi\)
0.466647 0.884444i \(-0.345462\pi\)
\(194\) −7.24264 + 12.5446i −0.519991 + 0.900651i
\(195\) 0 0
\(196\) −14.6569 + 25.3864i −1.04692 + 1.81332i
\(197\) −6.34315 −0.451930 −0.225965 0.974135i \(-0.572554\pi\)
−0.225965 + 0.974135i \(0.572554\pi\)
\(198\) 0 0
\(199\) 8.50000 14.7224i 0.602549 1.04365i −0.389885 0.920864i \(-0.627485\pi\)
0.992434 0.122782i \(-0.0391815\pi\)
\(200\) 2.20711 3.82282i 0.156066 0.270314i
\(201\) 0 0
\(202\) −38.9706 −2.74196
\(203\) 3.17157 5.49333i 0.222601 0.385556i
\(204\) 0 0
\(205\) −1.41421 + 2.44949i −0.0987730 + 0.171080i
\(206\) 5.03553 + 8.72180i 0.350842 + 0.607677i
\(207\) 0 0
\(208\) 11.4853 0.796361
\(209\) −11.3137 4.89898i −0.782586 0.338869i
\(210\) 0 0
\(211\) −11.1569 19.3242i −0.768070 1.33034i −0.938608 0.344984i \(-0.887884\pi\)
0.170539 0.985351i \(-0.445449\pi\)
\(212\) −3.82843 6.63103i −0.262937 0.455421i
\(213\) 0 0
\(214\) −16.8995 29.2708i −1.15523 2.00091i
\(215\) −1.08579 + 1.88064i −0.0740500 + 0.128258i
\(216\) 0 0
\(217\) 19.1421 1.29945
\(218\) 6.41421 11.1097i 0.434425 0.752447i
\(219\) 0 0
\(220\) −10.8284 −0.730052
\(221\) 26.1421 1.75851
\(222\) 0 0
\(223\) −0.0857864 0.148586i −0.00574468 0.00995009i 0.863139 0.504967i \(-0.168495\pi\)
−0.868883 + 0.495017i \(0.835162\pi\)
\(224\) 3.03553 5.25770i 0.202820 0.351295i
\(225\) 0 0
\(226\) −4.82843 8.36308i −0.321182 0.556304i
\(227\) −14.9706 −0.993631 −0.496816 0.867856i \(-0.665497\pi\)
−0.496816 + 0.867856i \(0.665497\pi\)
\(228\) 0 0
\(229\) 6.65685 0.439897 0.219949 0.975511i \(-0.429411\pi\)
0.219949 + 0.975511i \(0.429411\pi\)
\(230\) −5.82843 10.0951i −0.384315 0.665653i
\(231\) 0 0
\(232\) 3.65685 6.33386i 0.240084 0.415838i
\(233\) −1.34315 2.32640i −0.0879924 0.152407i 0.818670 0.574264i \(-0.194712\pi\)
−0.906662 + 0.421857i \(0.861378\pi\)
\(234\) 0 0
\(235\) 8.82843 0.575903
\(236\) 0 0
\(237\) 0 0
\(238\) −31.5563 + 54.6572i −2.04549 + 3.54290i
\(239\) −20.6274 −1.33428 −0.667138 0.744934i \(-0.732481\pi\)
−0.667138 + 0.744934i \(0.732481\pi\)
\(240\) 0 0
\(241\) −2.50000 + 4.33013i −0.161039 + 0.278928i −0.935242 0.354010i \(-0.884818\pi\)
0.774202 + 0.632938i \(0.218151\pi\)
\(242\) −3.62132 6.27231i −0.232787 0.403199i
\(243\) 0 0
\(244\) −27.3995 47.4573i −1.75407 3.03814i
\(245\) −3.82843 6.63103i −0.244589 0.423641i
\(246\) 0 0
\(247\) −13.3995 + 9.94655i −0.852589 + 0.632884i
\(248\) 22.0711 1.40151
\(249\) 0 0
\(250\) 1.20711 + 2.09077i 0.0763441 + 0.132232i
\(251\) −13.8284 + 23.9515i −0.872843 + 1.51181i −0.0137993 + 0.999905i \(0.504393\pi\)
−0.859043 + 0.511903i \(0.828941\pi\)
\(252\) 0 0
\(253\) −6.82843 + 11.8272i −0.429300 + 0.743569i
\(254\) 50.6274 3.17665
\(255\) 0 0
\(256\) 14.9853 25.9553i 0.936580 1.62220i
\(257\) −5.58579 + 9.67487i −0.348432 + 0.603502i −0.985971 0.166916i \(-0.946619\pi\)
0.637539 + 0.770418i \(0.279952\pi\)
\(258\) 0 0
\(259\) 29.9706 1.86228
\(260\) −7.32843 + 12.6932i −0.454490 + 0.787199i
\(261\) 0 0
\(262\) 12.6569 21.9223i 0.781943 1.35437i
\(263\) −6.89949 11.9503i −0.425441 0.736886i 0.571020 0.820936i \(-0.306548\pi\)
−0.996462 + 0.0840503i \(0.973214\pi\)
\(264\) 0 0
\(265\) 2.00000 0.122859
\(266\) −4.62132 40.0218i −0.283351 2.45389i
\(267\) 0 0
\(268\) 21.9853 + 38.0796i 1.34296 + 2.32608i
\(269\) −4.82843 8.36308i −0.294394 0.509906i 0.680449 0.732795i \(-0.261785\pi\)
−0.974844 + 0.222889i \(0.928451\pi\)
\(270\) 0 0
\(271\) −1.17157 2.02922i −0.0711680 0.123267i 0.828245 0.560365i \(-0.189339\pi\)
−0.899413 + 0.437099i \(0.856006\pi\)
\(272\) −10.2426 + 17.7408i −0.621051 + 1.07569i
\(273\) 0 0
\(274\) 15.6569 0.945865
\(275\) 1.41421 2.44949i 0.0852803 0.147710i
\(276\) 0 0
\(277\) 6.00000 0.360505 0.180253 0.983620i \(-0.442309\pi\)
0.180253 + 0.983620i \(0.442309\pi\)
\(278\) −15.2426 −0.914193
\(279\) 0 0
\(280\) −8.44975 14.6354i −0.504969 0.874632i
\(281\) 13.4853 23.3572i 0.804464 1.39337i −0.112188 0.993687i \(-0.535786\pi\)
0.916652 0.399686i \(-0.130881\pi\)
\(282\) 0 0
\(283\) −6.48528 11.2328i −0.385510 0.667723i 0.606330 0.795213i \(-0.292641\pi\)
−0.991840 + 0.127490i \(0.959308\pi\)
\(284\) −38.2843 −2.27175
\(285\) 0 0
\(286\) 26.1421 1.54582
\(287\) 5.41421 + 9.37769i 0.319591 + 0.553548i
\(288\) 0 0
\(289\) −14.8137 + 25.6581i −0.871395 + 1.50930i
\(290\) 2.00000 + 3.46410i 0.117444 + 0.203419i
\(291\) 0 0
\(292\) −28.6569 −1.67702
\(293\) −17.3137 −1.01148 −0.505739 0.862687i \(-0.668780\pi\)
−0.505739 + 0.862687i \(0.668780\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 34.5563 2.00855
\(297\) 0 0
\(298\) 8.24264 14.2767i 0.477483 0.827025i
\(299\) 9.24264 + 16.0087i 0.534516 + 0.925808i
\(300\) 0 0
\(301\) 4.15685 + 7.19988i 0.239597 + 0.414994i
\(302\) 26.1421 + 45.2795i 1.50431 + 2.60554i
\(303\) 0 0
\(304\) −1.50000 12.9904i −0.0860309 0.745049i
\(305\) 14.3137 0.819601
\(306\) 0 0
\(307\) 3.17157 + 5.49333i 0.181011 + 0.313521i 0.942225 0.334980i \(-0.108730\pi\)
−0.761214 + 0.648501i \(0.775396\pi\)
\(308\) −20.7279 + 35.9018i −1.18108 + 2.04570i
\(309\) 0 0
\(310\) −6.03553 + 10.4539i −0.342795 + 0.593739i
\(311\) 4.00000 0.226819 0.113410 0.993548i \(-0.463823\pi\)
0.113410 + 0.993548i \(0.463823\pi\)
\(312\) 0 0
\(313\) 3.00000 5.19615i 0.169570 0.293704i −0.768699 0.639611i \(-0.779095\pi\)
0.938269 + 0.345907i \(0.112429\pi\)
\(314\) −17.1066 + 29.6295i −0.965381 + 1.67209i
\(315\) 0 0
\(316\) −56.1127 −3.15659
\(317\) −8.65685 + 14.9941i −0.486217 + 0.842153i −0.999875 0.0158423i \(-0.994957\pi\)
0.513657 + 0.857996i \(0.328290\pi\)
\(318\) 0 0
\(319\) 2.34315 4.05845i 0.131191 0.227229i
\(320\) 4.91421 + 8.51167i 0.274713 + 0.475817i
\(321\) 0 0
\(322\) −44.6274 −2.48699
\(323\) −3.41421 29.5680i −0.189972 1.64521i
\(324\) 0 0
\(325\) −1.91421 3.31552i −0.106181 0.183912i
\(326\) −15.8640 27.4772i −0.878624 1.52182i
\(327\) 0 0
\(328\) 6.24264 + 10.8126i 0.344692 + 0.597024i
\(329\) 16.8995 29.2708i 0.931699 1.61375i
\(330\) 0 0
\(331\) −16.6569 −0.915544 −0.457772 0.889070i \(-0.651352\pi\)
−0.457772 + 0.889070i \(0.651352\pi\)
\(332\) −15.3137 + 26.5241i −0.840449 + 1.45570i
\(333\) 0 0
\(334\) 21.6569 1.18501
\(335\) −11.4853 −0.627508
\(336\) 0 0
\(337\) −0.257359 0.445759i −0.0140193 0.0242821i 0.858931 0.512092i \(-0.171129\pi\)
−0.872950 + 0.487810i \(0.837796\pi\)
\(338\) 2.00000 3.46410i 0.108786 0.188422i
\(339\) 0 0
\(340\) −13.0711 22.6398i −0.708878 1.22781i
\(341\) 14.1421 0.765840
\(342\) 0 0
\(343\) −2.51472 −0.135782
\(344\) 4.79289 + 8.30153i 0.258415 + 0.447589i
\(345\) 0 0
\(346\) 18.4853 32.0174i 0.993775 1.72127i
\(347\) 7.72792 + 13.3852i 0.414857 + 0.718553i 0.995413 0.0956671i \(-0.0304984\pi\)
−0.580557 + 0.814220i \(0.697165\pi\)
\(348\) 0 0
\(349\) 13.6274 0.729459 0.364729 0.931114i \(-0.381161\pi\)
0.364729 + 0.931114i \(0.381161\pi\)
\(350\) 9.24264 0.494040
\(351\) 0 0
\(352\) 2.24264 3.88437i 0.119533 0.207037i
\(353\) −21.3137 −1.13441 −0.567207 0.823575i \(-0.691976\pi\)
−0.567207 + 0.823575i \(0.691976\pi\)
\(354\) 0 0
\(355\) 5.00000 8.66025i 0.265372 0.459639i
\(356\) −8.58579 14.8710i −0.455046 0.788162i
\(357\) 0 0
\(358\) 14.6569 + 25.3864i 0.774639 + 1.34171i
\(359\) 7.41421 + 12.8418i 0.391307 + 0.677764i 0.992622 0.121248i \(-0.0386896\pi\)
−0.601315 + 0.799012i \(0.705356\pi\)
\(360\) 0 0
\(361\) 13.0000 + 13.8564i 0.684211 + 0.729285i
\(362\) −6.48528 −0.340859
\(363\) 0 0
\(364\) 28.0563 + 48.5950i 1.47055 + 2.54707i
\(365\) 3.74264 6.48244i 0.195899 0.339307i
\(366\) 0 0
\(367\) −14.0563 + 24.3463i −0.733735 + 1.27087i 0.221540 + 0.975151i \(0.428892\pi\)
−0.955276 + 0.295716i \(0.904442\pi\)
\(368\) −14.4853 −0.755097
\(369\) 0 0
\(370\) −9.44975 + 16.3674i −0.491269 + 0.850903i
\(371\) 3.82843 6.63103i 0.198762 0.344266i
\(372\) 0 0
\(373\) −0.343146 −0.0177674 −0.00888371 0.999961i \(-0.502828\pi\)
−0.00888371 + 0.999961i \(0.502828\pi\)
\(374\) −23.3137 + 40.3805i −1.20552 + 2.08803i
\(375\) 0 0
\(376\) 19.4853 33.7495i 1.00488 1.74050i
\(377\) −3.17157 5.49333i −0.163344 0.282921i
\(378\) 0 0
\(379\) 24.3137 1.24891 0.624456 0.781060i \(-0.285321\pi\)
0.624456 + 0.781060i \(0.285321\pi\)
\(380\) 15.3137 + 6.63103i 0.785577 + 0.340165i
\(381\) 0 0
\(382\) 13.4853 + 23.3572i 0.689967 + 1.19506i
\(383\) 16.9706 + 29.3939i 0.867155 + 1.50196i 0.864891 + 0.501960i \(0.167387\pi\)
0.00226413 + 0.999997i \(0.499279\pi\)
\(384\) 0 0
\(385\) −5.41421 9.37769i −0.275934 0.477931i
\(386\) 17.8640 30.9413i 0.909252 1.57487i
\(387\) 0 0
\(388\) −22.9706 −1.16615
\(389\) 17.7279 30.7057i 0.898841 1.55684i 0.0698641 0.997557i \(-0.477743\pi\)
0.828977 0.559282i \(-0.188923\pi\)
\(390\) 0 0
\(391\) −32.9706 −1.66739
\(392\) −33.7990 −1.70711
\(393\) 0 0
\(394\) −7.65685 13.2621i −0.385747 0.668133i
\(395\) 7.32843 12.6932i 0.368733 0.638665i
\(396\) 0 0
\(397\) 9.08579 + 15.7370i 0.456003 + 0.789820i 0.998745 0.0500794i \(-0.0159475\pi\)
−0.542743 + 0.839899i \(0.682614\pi\)
\(398\) 41.0416 2.05723
\(399\) 0 0
\(400\) 3.00000 0.150000
\(401\) 11.3137 + 19.5959i 0.564980 + 0.978573i 0.997052 + 0.0767343i \(0.0244493\pi\)
−0.432072 + 0.901839i \(0.642217\pi\)
\(402\) 0 0
\(403\) 9.57107 16.5776i 0.476769 0.825788i
\(404\) −30.8995 53.5195i −1.53731 2.66269i
\(405\) 0 0
\(406\) 15.3137 0.760007
\(407\) 22.1421 1.09754
\(408\) 0 0
\(409\) −3.00000 + 5.19615i −0.148340 + 0.256933i −0.930614 0.366002i \(-0.880726\pi\)
0.782274 + 0.622935i \(0.214060\pi\)
\(410\) −6.82843 −0.337232
\(411\) 0 0
\(412\) −7.98528 + 13.8309i −0.393407 + 0.681400i
\(413\) 0 0
\(414\) 0 0
\(415\) −4.00000 6.92820i −0.196352 0.340092i
\(416\) −3.03553 5.25770i −0.148829 0.257780i
\(417\) 0 0
\(418\) −3.41421 29.5680i −0.166995 1.44622i
\(419\) 19.3137 0.943536 0.471768 0.881723i \(-0.343616\pi\)
0.471768 + 0.881723i \(0.343616\pi\)
\(420\) 0 0
\(421\) −1.82843 3.16693i −0.0891121 0.154347i 0.818024 0.575184i \(-0.195070\pi\)
−0.907136 + 0.420837i \(0.861736\pi\)
\(422\) 26.9350 46.6528i 1.31118 2.27102i
\(423\) 0 0
\(424\) 4.41421 7.64564i 0.214373 0.371305i
\(425\) 6.82843 0.331227
\(426\) 0 0
\(427\) 27.3995 47.4573i 1.32595 2.29662i
\(428\) 26.7990 46.4172i 1.29538 2.24366i
\(429\) 0 0
\(430\) −5.24264 −0.252823
\(431\) 7.24264 12.5446i 0.348866 0.604253i −0.637183 0.770713i \(-0.719900\pi\)
0.986048 + 0.166460i \(0.0532336\pi\)
\(432\) 0 0
\(433\) 17.0858 29.5935i 0.821090 1.42217i −0.0837804 0.996484i \(-0.526699\pi\)
0.904871 0.425686i \(-0.139967\pi\)
\(434\) 23.1066 + 40.0218i 1.10915 + 1.92111i
\(435\) 0 0
\(436\) 20.3431 0.974260
\(437\) 16.8995 12.5446i 0.808412 0.600091i
\(438\) 0 0
\(439\) −8.50000 14.7224i −0.405683 0.702663i 0.588718 0.808339i \(-0.299633\pi\)
−0.994401 + 0.105675i \(0.966300\pi\)
\(440\) −6.24264 10.8126i −0.297606 0.515469i
\(441\) 0 0
\(442\) 31.5563 + 54.6572i 1.50098 + 2.59978i
\(443\) −5.07107 + 8.78335i −0.240934 + 0.417309i −0.960981 0.276616i \(-0.910787\pi\)
0.720047 + 0.693925i \(0.244120\pi\)
\(444\) 0 0
\(445\) 4.48528 0.212623
\(446\) 0.207107 0.358719i 0.00980679 0.0169859i
\(447\) 0 0
\(448\) 37.6274 1.77773
\(449\) −18.8284 −0.888568 −0.444284 0.895886i \(-0.646542\pi\)
−0.444284 + 0.895886i \(0.646542\pi\)
\(450\) 0 0
\(451\) 4.00000 + 6.92820i 0.188353 + 0.326236i
\(452\) 7.65685 13.2621i 0.360148 0.623795i
\(453\) 0 0
\(454\) −18.0711 31.3000i −0.848117 1.46898i
\(455\) −14.6569 −0.687124
\(456\) 0 0
\(457\) −9.82843 −0.459754 −0.229877 0.973220i \(-0.573832\pi\)
−0.229877 + 0.973220i \(0.573832\pi\)
\(458\) 8.03553 + 13.9180i 0.375476 + 0.650343i
\(459\) 0 0
\(460\) 9.24264 16.0087i 0.430940 0.746411i
\(461\) 0.928932 + 1.60896i 0.0432647 + 0.0749366i 0.886847 0.462064i \(-0.152891\pi\)
−0.843582 + 0.537000i \(0.819557\pi\)
\(462\) 0 0
\(463\) 16.7990 0.780715 0.390358 0.920663i \(-0.372351\pi\)
0.390358 + 0.920663i \(0.372351\pi\)
\(464\) 4.97056 0.230753
\(465\) 0 0
\(466\) 3.24264 5.61642i 0.150212 0.260176i
\(467\) 15.7990 0.731090 0.365545 0.930794i \(-0.380883\pi\)
0.365545 + 0.930794i \(0.380883\pi\)
\(468\) 0 0
\(469\) −21.9853 + 38.0796i −1.01519 + 1.75835i
\(470\) 10.6569 + 18.4582i 0.491564 + 0.851414i
\(471\) 0 0
\(472\) 0 0
\(473\) 3.07107 + 5.31925i 0.141208 + 0.244579i
\(474\) 0 0
\(475\) −3.50000 + 2.59808i −0.160591 + 0.119208i
\(476\) −100.083 −4.58731
\(477\) 0 0
\(478\) −24.8995 43.1272i −1.13888 1.97259i
\(479\) −7.24264 + 12.5446i −0.330925 + 0.573178i −0.982693 0.185239i \(-0.940694\pi\)
0.651769 + 0.758418i \(0.274027\pi\)
\(480\) 0 0
\(481\) 14.9853 25.9553i 0.683270 1.18346i
\(482\) −12.0711 −0.549822
\(483\) 0 0
\(484\) 5.74264 9.94655i 0.261029 0.452116i
\(485\) 3.00000 5.19615i 0.136223 0.235945i
\(486\) 0 0
\(487\) −17.6569 −0.800108 −0.400054 0.916491i \(-0.631009\pi\)
−0.400054 + 0.916491i \(0.631009\pi\)
\(488\) 31.5919 54.7187i 1.43010 2.47700i
\(489\) 0 0
\(490\) 9.24264 16.0087i 0.417540 0.723200i
\(491\) 6.17157 + 10.6895i 0.278519 + 0.482409i 0.971017 0.239011i \(-0.0768231\pi\)
−0.692498 + 0.721420i \(0.743490\pi\)
\(492\) 0 0
\(493\) 11.3137 0.509544
\(494\) −36.9706 16.0087i −1.66338 0.720267i
\(495\) 0 0
\(496\) 7.50000 + 12.9904i 0.336760 + 0.583285i
\(497\) −19.1421 33.1552i −0.858642 1.48721i
\(498\) 0 0
\(499\) 9.32843 + 16.1573i 0.417598 + 0.723301i 0.995697 0.0926657i \(-0.0295388\pi\)
−0.578100 + 0.815966i \(0.696205\pi\)
\(500\) −1.91421 + 3.31552i −0.0856062 + 0.148274i
\(501\) 0 0
\(502\) −66.7696 −2.98007
\(503\) 21.0711 36.4962i 0.939512 1.62728i 0.173130 0.984899i \(-0.444612\pi\)
0.766383 0.642384i \(-0.222055\pi\)
\(504\) 0 0
\(505\) 16.1421 0.718316
\(506\) −32.9706 −1.46572
\(507\) 0 0
\(508\) 40.1421 + 69.5282i 1.78102 + 3.08482i
\(509\) −14.5563 + 25.2123i −0.645199 + 1.11752i 0.339057 + 0.940766i \(0.389892\pi\)
−0.984256 + 0.176751i \(0.943441\pi\)
\(510\) 0 0
\(511\) −14.3284 24.8176i −0.633852 1.09786i
\(512\) 31.2426 1.38074
\(513\) 0 0
\(514\) −26.9706 −1.18962
\(515\) −2.08579 3.61269i −0.0919107 0.159194i
\(516\) 0 0
\(517\) 12.4853 21.6251i 0.549102 0.951073i
\(518\) 36.1777 + 62.6616i 1.58956 + 2.75319i
\(519\) 0 0
\(520\) −16.8995 −0.741092
\(521\) −17.6569 −0.773561 −0.386780 0.922172i \(-0.626413\pi\)
−0.386780 + 0.922172i \(0.626413\pi\)
\(522\) 0 0
\(523\) −21.8848 + 37.9055i −0.956954 + 1.65749i −0.227124 + 0.973866i \(0.572932\pi\)
−0.729831 + 0.683628i \(0.760401\pi\)
\(524\) 40.1421 1.75362
\(525\) 0 0
\(526\) 16.6569 28.8505i 0.726273 1.25794i
\(527\) 17.0711 + 29.5680i 0.743627 + 1.28800i
\(528\) 0 0
\(529\) −0.156854 0.271680i −0.00681975 0.0118122i
\(530\) 2.41421 + 4.18154i 0.104867 + 0.181635i
\(531\) 0 0
\(532\) 51.2990 38.0796i 2.22409 1.65096i
\(533\) 10.8284 0.469031
\(534\) 0 0
\(535\) 7.00000 + 12.1244i 0.302636 + 0.524182i
\(536\) −25.3492 + 43.9062i −1.09492 + 1.89646i
\(537\) 0 0
\(538\) 11.6569 20.1903i 0.502563 0.870464i
\(539\) −21.6569 −0.932827
\(540\) 0 0
\(541\) 3.15685 5.46783i 0.135724 0.235080i −0.790150 0.612914i \(-0.789997\pi\)
0.925874 + 0.377833i \(0.123331\pi\)
\(542\) 2.82843 4.89898i 0.121491 0.210429i
\(543\) 0 0
\(544\) 10.8284 0.464265
\(545\) −2.65685 + 4.60181i −0.113807 + 0.197120i
\(546\) 0 0
\(547\) −7.57107 + 13.1135i −0.323715 + 0.560692i −0.981252 0.192731i \(-0.938265\pi\)
0.657536 + 0.753423i \(0.271599\pi\)
\(548\) 12.4142 + 21.5020i 0.530309 + 0.918522i
\(549\) 0 0
\(550\) 6.82843 0.291165
\(551\) −5.79899 + 4.30463i −0.247045 + 0.183384i
\(552\) 0 0
\(553\) −28.0563 48.5950i −1.19308 2.06647i
\(554\) 7.24264 + 12.5446i 0.307710 + 0.532970i
\(555\) 0 0
\(556\) −12.0858 20.9332i −0.512552 0.887765i
\(557\) −21.4853 + 37.2136i −0.910361 + 1.57679i −0.0968052 + 0.995303i \(0.530862\pi\)
−0.813555 + 0.581487i \(0.802471\pi\)
\(558\) 0 0
\(559\) 8.31371 0.351632
\(560\) 5.74264 9.94655i 0.242671 0.420318i
\(561\) 0 0
\(562\) 65.1127 2.74661
\(563\) −16.1421 −0.680310 −0.340155 0.940369i \(-0.610480\pi\)
−0.340155 + 0.940369i \(0.610480\pi\)
\(564\) 0 0
\(565\) 2.00000 + 3.46410i 0.0841406 + 0.145736i
\(566\) 15.6569 27.1185i 0.658107 1.13987i
\(567\) 0 0
\(568\) −22.0711 38.2282i −0.926081 1.60402i
\(569\) 28.9706 1.21451 0.607255 0.794507i \(-0.292271\pi\)
0.607255 + 0.794507i \(0.292271\pi\)
\(570\) 0 0
\(571\) −8.31371 −0.347918 −0.173959 0.984753i \(-0.555656\pi\)
−0.173959 + 0.984753i \(0.555656\pi\)
\(572\) 20.7279 + 35.9018i 0.866678 + 1.50113i
\(573\) 0 0
\(574\) −13.0711 + 22.6398i −0.545576 + 0.944965i
\(575\) 2.41421 + 4.18154i 0.100680 + 0.174382i
\(576\) 0 0
\(577\) −47.6569 −1.98398 −0.991990 0.126313i \(-0.959686\pi\)
−0.991990 + 0.126313i \(0.959686\pi\)
\(578\) −71.5269 −2.97513
\(579\) 0 0
\(580\) −3.17157 + 5.49333i −0.131692 + 0.228098i
\(581\) −30.6274 −1.27064
\(582\) 0 0
\(583\) 2.82843 4.89898i 0.117141 0.202895i
\(584\) −16.5208 28.6149i −0.683636 1.18409i
\(585\) 0 0
\(586\) −20.8995 36.1990i −0.863350 1.49537i
\(587\) −17.3137 29.9882i −0.714613 1.23775i −0.963109 0.269113i \(-0.913269\pi\)
0.248495 0.968633i \(-0.420064\pi\)
\(588\) 0 0
\(589\) −20.0000 8.66025i −0.824086 0.356840i
\(590\) 0 0
\(591\) 0 0
\(592\) 11.7426 + 20.3389i 0.482620 + 0.835922i
\(593\) −19.0711 + 33.0321i −0.783155 + 1.35646i 0.146940 + 0.989145i \(0.453057\pi\)
−0.930095 + 0.367319i \(0.880276\pi\)
\(594\) 0 0
\(595\) 13.0711 22.6398i 0.535862 0.928139i
\(596\) 26.1421 1.07082
\(597\) 0 0
\(598\) −22.3137 + 38.6485i −0.912475 + 1.58045i
\(599\) 8.48528 14.6969i 0.346699 0.600501i −0.638962 0.769238i \(-0.720636\pi\)
0.985661 + 0.168738i \(0.0539691\pi\)
\(600\) 0 0
\(601\) −46.6569 −1.90317 −0.951586 0.307381i \(-0.900547\pi\)
−0.951586 + 0.307381i \(0.900547\pi\)
\(602\) −10.0355 + 17.3821i −0.409018 + 0.708440i
\(603\) 0 0
\(604\) −41.4558 + 71.8036i −1.68681 + 2.92165i
\(605\) 1.50000 + 2.59808i 0.0609837 + 0.105627i
\(606\) 0 0
\(607\) −11.8284 −0.480101 −0.240051 0.970760i \(-0.577164\pi\)
−0.240051 + 0.970760i \(0.577164\pi\)
\(608\) −5.55025 + 4.11999i −0.225092 + 0.167088i
\(609\) 0 0
\(610\) 17.2782 + 29.9267i 0.699573 + 1.21170i
\(611\) −16.8995 29.2708i −0.683680 1.18417i
\(612\) 0 0
\(613\) 22.7990 + 39.4890i 0.920843 + 1.59495i 0.798115 + 0.602506i \(0.205831\pi\)
0.122728 + 0.992440i \(0.460836\pi\)
\(614\) −7.65685 + 13.2621i −0.309005 + 0.535213i
\(615\) 0 0
\(616\) −47.7990 −1.92588
\(617\) 7.17157 12.4215i 0.288717 0.500072i −0.684787 0.728743i \(-0.740105\pi\)
0.973504 + 0.228671i \(0.0734381\pi\)
\(618\) 0 0
\(619\) 38.3137 1.53996 0.769979 0.638069i \(-0.220267\pi\)
0.769979 + 0.638069i \(0.220267\pi\)
\(620\) −19.1421 −0.768767
\(621\) 0 0
\(622\) 4.82843 + 8.36308i 0.193602 + 0.335329i
\(623\) 8.58579 14.8710i 0.343982 0.595795i
\(624\) 0 0
\(625\) −0.500000 0.866025i −0.0200000 0.0346410i
\(626\) 14.4853 0.578948
\(627\) 0 0
\(628\) −54.2548 −2.16500
\(629\) 26.7279 + 46.2941i 1.06571 + 1.84587i
\(630\) 0 0
\(631\) −21.6421 + 37.4853i −0.861560 + 1.49227i 0.00886314 + 0.999961i \(0.497179\pi\)
−0.870423 + 0.492305i \(0.836155\pi\)
\(632\) −32.3492 56.0305i −1.28678 2.22877i
\(633\) 0 0
\(634\) −41.7990 −1.66005
\(635\) −20.9706 −0.832191
\(636\) 0 0
\(637\) −14.6569 + 25.3864i −0.580726 + 1.00585i
\(638\) 11.3137 0.447914
\(639\) 0 0
\(640\) −10.2782 + 17.8023i −0.406281 + 0.703699i
\(641\) −0.0710678 0.123093i −0.00280701 0.00486188i 0.864618 0.502429i \(-0.167560\pi\)
−0.867425 + 0.497567i \(0.834227\pi\)
\(642\) 0 0
\(643\) −0.0857864 0.148586i −0.00338309 0.00585968i 0.864329 0.502927i \(-0.167744\pi\)
−0.867712 + 0.497067i \(0.834410\pi\)
\(644\) −35.3848 61.2882i −1.39436 2.41509i
\(645\) 0 0
\(646\) 57.6985 42.8300i 2.27012 1.68512i
\(647\) −24.2843 −0.954713 −0.477357 0.878710i \(-0.658405\pi\)
−0.477357 + 0.878710i \(0.658405\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) 4.62132 8.00436i 0.181263 0.313957i
\(651\) 0 0
\(652\) 25.1569 43.5729i 0.985218 1.70645i
\(653\) 27.9411 1.09342 0.546710 0.837322i \(-0.315880\pi\)
0.546710 + 0.837322i \(0.315880\pi\)
\(654\) 0 0
\(655\) −5.24264 + 9.08052i −0.204847 + 0.354805i
\(656\) −4.24264 + 7.34847i −0.165647 + 0.286910i
\(657\) 0 0
\(658\) 81.5980 3.18102
\(659\) 12.2426 21.2049i 0.476906 0.826025i −0.522744 0.852490i \(-0.675092\pi\)
0.999650 + 0.0264649i \(0.00842503\pi\)
\(660\) 0 0
\(661\) −13.4853 + 23.3572i −0.524517 + 0.908489i 0.475076 + 0.879945i \(0.342421\pi\)
−0.999593 + 0.0285447i \(0.990913\pi\)
\(662\) −20.1066 34.8257i −0.781465 1.35354i
\(663\) 0 0
\(664\) −35.3137 −1.37044
\(665\) 1.91421 + 16.5776i 0.0742300 + 0.642851i
\(666\) 0 0
\(667\) 4.00000 + 6.92820i 0.154881 + 0.268261i
\(668\) 17.1716 + 29.7420i 0.664388 + 1.15075i
\(669\) 0 0
\(670\) −13.8640 24.0131i −0.535612 0.927706i
\(671\) 20.2426 35.0613i 0.781458 1.35353i
\(672\) 0 0
\(673\) −18.1716 −0.700463 −0.350231 0.936663i \(-0.613897\pi\)
−0.350231 + 0.936663i \(0.613897\pi\)
\(674\) 0.621320 1.07616i 0.0239324 0.0414521i
\(675\) 0 0
\(676\) 6.34315 0.243967
\(677\) −27.4558 −1.05521 −0.527607 0.849489i \(-0.676911\pi\)
−0.527607 + 0.849489i \(0.676911\pi\)
\(678\) 0 0
\(679\) −11.4853 19.8931i −0.440765 0.763427i
\(680\) 15.0711 26.1039i 0.577949 1.00104i
\(681\) 0 0
\(682\) 17.0711 + 29.5680i 0.653685 + 1.13222i
\(683\) −15.8579 −0.606784 −0.303392 0.952866i \(-0.598119\pi\)
−0.303392 + 0.952866i \(0.598119\pi\)
\(684\) 0 0
\(685\) −6.48528 −0.247790
\(686\) −3.03553 5.25770i −0.115897 0.200740i
\(687\) 0 0
\(688\) −3.25736 + 5.64191i −0.124186 + 0.215096i
\(689\) −3.82843 6.63103i −0.145851 0.252622i
\(690\) 0 0
\(691\) 8.68629 0.330442 0.165221 0.986257i \(-0.447166\pi\)
0.165221 + 0.986257i \(0.447166\pi\)
\(692\) 58.6274 2.22868
\(693\) 0 0
\(694\) −18.6569 + 32.3146i −0.708205 + 1.22665i
\(695\) 6.31371 0.239493
\(696\) 0 0
\(697\) −9.65685 + 16.7262i −0.365779 + 0.633549i
\(698\) 16.4497 + 28.4918i 0.622632 + 1.07843i
\(699\) 0 0
\(700\) 7.32843 + 12.6932i 0.276989 + 0.479758i
\(701\) 1.92893 + 3.34101i 0.0728548 + 0.126188i 0.900151 0.435577i \(-0.143456\pi\)
−0.827297 + 0.561765i \(0.810122\pi\)
\(702\) 0 0
\(703\) −31.3137 13.5592i −1.18102 0.511396i
\(704\) 27.7990 1.04771
\(705\) 0 0
\(706\) −25.7279 44.5621i −0.968283 1.67712i
\(707\) 30.8995 53.5195i 1.16210 2.01281i
\(708\) 0 0
\(709\) 6.81371 11.8017i 0.255894 0.443222i −0.709244 0.704963i \(-0.750963\pi\)
0.965138 + 0.261742i \(0.0842968\pi\)
\(710\) 24.1421 0.906038
\(711\) 0 0
\(712\) 9.89949 17.1464i 0.370999 0.642590i
\(713\) −12.0711 + 20.9077i −0.452065 + 0.783000i
\(714\) 0 0
\(715\) −10.8284 −0.404960
\(716\) −23.2426 + 40.2574i −0.868618 + 1.50449i
\(717\) 0 0
\(718\) −17.8995 + 31.0028i −0.668003 + 1.15702i
\(719\) −14.4142 24.9662i −0.537559 0.931080i −0.999035 0.0439272i \(-0.986013\pi\)
0.461475 0.887153i \(-0.347320\pi\)
\(720\) 0 0
\(721\) −15.9706 −0.594775
\(722\) −13.2782 + 43.9062i −0.494162 + 1.63402i
\(723\) 0 0
\(724\) −5.14214 8.90644i −0.191106 0.331005i
\(725\) −0.828427 1.43488i −0.0307670 0.0532900i
\(726\) 0 0
\(727\) −20.9142 36.2245i −0.775665 1.34349i −0.934420 0.356174i \(-0.884081\pi\)
0.158755 0.987318i \(-0.449252\pi\)
\(728\) −32.3492 + 56.0305i −1.19894 + 2.07663i
\(729\) 0 0
\(730\) 18.0711 0.668840
\(731\) −7.41421 + 12.8418i −0.274225 + 0.474971i
\(732\) 0 0
\(733\) −7.65685 −0.282812 −0.141406 0.989952i \(-0.545162\pi\)
−0.141406 + 0.989952i \(0.545162\pi\)
\(734\) −67.8701 −2.50513
\(735\) 0 0
\(736\) 3.82843 + 6.63103i 0.141118 + 0.244423i
\(737\) −16.2426 + 28.1331i −0.598305 + 1.03630i
\(738\) 0 0
\(739\) −1.81371 3.14144i −0.0667183 0.115560i 0.830737 0.556666i \(-0.187920\pi\)
−0.897455 + 0.441106i \(0.854586\pi\)
\(740\) −29.9706 −1.10174
\(741\) 0 0
\(742\) 18.4853 0.678616
\(743\) 2.92893 + 5.07306i 0.107452 + 0.186112i 0.914737 0.404049i \(-0.132397\pi\)
−0.807285 + 0.590161i \(0.799064\pi\)
\(744\) 0 0
\(745\) −3.41421 + 5.91359i −0.125087 + 0.216657i
\(746\) −0.414214 0.717439i −0.0151654 0.0262673i
\(747\) 0 0
\(748\) −73.9411 −2.70356
\(749\) 53.5980 1.95843
\(750\) 0 0
\(751\) −1.84315 + 3.19242i −0.0672573 + 0.116493i −0.897693 0.440621i \(-0.854758\pi\)
0.830436 + 0.557114i \(0.188092\pi\)
\(752\) 26.4853 0.965819
\(753\) 0 0
\(754\) 7.65685 13.2621i 0.278846 0.482976i
\(755\) −10.8284 18.7554i −0.394087 0.682578i
\(756\) 0 0
\(757\) 2.42893 + 4.20703i 0.0882810 + 0.152907i 0.906785 0.421594i \(-0.138529\pi\)
−0.818504 + 0.574501i \(0.805196\pi\)
\(758\) 29.3492 + 50.8344i 1.06601 + 1.84639i
\(759\) 0 0
\(760\) 2.20711 + 19.1141i 0.0800602 + 0.693341i
\(761\) 27.5980 1.00043 0.500213 0.865902i \(-0.333255\pi\)
0.500213 + 0.865902i \(0.333255\pi\)
\(762\) 0 0
\(763\) 10.1716 + 17.6177i 0.368236 + 0.637803i
\(764\) −21.3848 + 37.0395i −0.773674 + 1.34004i
\(765\) 0 0
\(766\) −40.9706 + 70.9631i −1.48033 + 2.56400i
\(767\) 0 0
\(768\) 0 0
\(769\) 4.15685 7.19988i 0.149900 0.259634i −0.781290 0.624168i \(-0.785438\pi\)
0.931190 + 0.364533i \(0.118771\pi\)
\(770\) 13.0711 22.6398i 0.471049 0.815880i
\(771\) 0 0
\(772\) 56.6569 2.03912
\(773\) −11.0000 + 19.0526i −0.395643 + 0.685273i −0.993183 0.116566i \(-0.962811\pi\)
0.597540 + 0.801839i \(0.296145\pi\)
\(774\) 0 0
\(775\) 2.50000 4.33013i 0.0898027 0.155543i
\(776\) −13.2426 22.9369i −0.475383 0.823388i
\(777\) 0 0
\(778\) 85.5980 3.06884
\(779\) −1.41421 12.2474i −0.0506695 0.438810i
\(780\) 0 0
\(781\) −14.1421 24.4949i −0.506045 0.876496i
\(782\) −39.7990 68.9339i −1.42321 2.46507i
\(783\) 0 0